The Asus note is quite vague when it says it removes the 4th generation support when using a 3000 series CPU.
I was able to find an old Overclock3D.net thread (2019) where a AMD Employee explains what the above means: https://forum.overclock3d.net/showthread.php?t=92928
If you noticed the previous BIOS version at Asus Support, the first time the above is mentioned, is on BIOS Version 5216 on 09/09/2019.
That is when the 4th Generation PCIe option was removed from BIOS on your Asus Motherboard.
It means that it will remove Generation 4 PCIe support from the motherboard. It has nothing to do with supporting a CPU or not. Your Ryzen 5 3600 should work fine with the latest BIOS version you have installed.
If a CPU will lose support on a Motherboard BIOS update it will definitely let you know. It will says CPUs series so and so (Raven Ridge, pinnacle, etc) will have support removed with this BIOS update.